This comprehensive text introduces the analysis of the semantics of programming languages and programming logics. It discusses denotational, operational, and axiomatic approaches and the relations between them in a unified framework. Organized around analysis of three languages - the simple imperative language of while commands, a simple applicative language based on the typed lambda calculus, and an Algol-like language which is an extension of the simple languages, the text discusses syntactic and semantic methods appropriate to typed languages. There also self-contained introductions to natural deduction, domain theory, and category theory, and a discussion of modern techniques of possible worlds.